Three Molecules Of Type A ,three Of Type B, Three Of Type Ck And Three Of Type D Are To Be Linked Together To Form A Chain Molecule. One Such Chain Molecule Is Abcdabcdabcd, And Another Is Bcddaaabdbcc.
(a) How Many Such Chain Molecules Are There? {hints: If The Three A's Were Distinguishable From One Another A1,a2,a3------and The B's And C's And D's Werealso, How Many Molecules Would There Be?

Let's start with the second part first. If each of the molecules are distinguishable, that means you have 12 distinct molecules to be placed into the 12-molecule chain. So for the first position in the chain you have 12 possibilities. Then for the second position you have 11 molecules left to choose from, and so on. Continue for all 12 positions, and you see that there are 12! Ways to put the chain together. However, there's a trick - it would seem that if a chain reads left-to-right in a particular sequence it is identical to a chain the reads right-to-left in the same sequence. For example, the chain ABCD is identical to the chain DCBA, since you can just turn one around to get the other. Thus you need to divide the number we got above by 2 .

Now, if the molecule types are indistinguishable, that means each of the 3 A's have 3! =6 different ways they can be arranged that are all indistinguishable. Same thing for the B's, C's, and D's. So now can you figure out how much to divide the answer above to account for this? Post back and let us know what you get.